```Date: Nov 17, 2012 11:55 PM
Author: Graham Cooper
Subject: Re: A HARD FLAW in Godel's Proof

On Nov 18, 1:10 pm, "INFINITY POWER" <infin...@limited.com> wrote:> THINKING CAPS ON!> ARGUE LOGICALLY!> ASSUME ANYTHING!> ROLLBACK ASSUMPTIONS LATER ON <<!>> STEP 1:  DEFINE a 2 parameter predicate DERIVE(THEOREM, DERIVATION)>> DERIVE(T,D) is TRUE IFF>   D contains a sequence of inference rules and substitutions>   and the final formula T in D is logically implied from the Axioms.>> - - - - - - - - - - - - - ->> STEP 2:  DEFINE a Godel Statement.>> i.e.  Godel Statement named G =>     ALL(M)  ~DERIVE(G,M)>> - - - - - - - - - - - - - ->> STEP 3:  IS G A THEOREM?>> ASSUME: YES G IS A THEOREM>     DERIVE(   G:ALL(M)~DERIVE(G,M)  , D )>> - - - - - - - - - - - - - ->> STEP 4:  UNIFY THE QUERY TO THE AXIOMS TO GET THE ANSWER>>   GOAL :       DERIVE(  G:ALL(M)~DERIVE(G,M)   , D )>   SUBGOAL :    G:ALL(M)~DERIVE(G,M)>>   (SUBGOALs are a Derivation Process that calculate reverse D in the trace)>> - - - - - - - - - - - - - - ->> STEP 5:  REMOVE THE QUANTIFIER>>   G:~EXIST(M)DERIVE(G,M)>   G: ~DERIVE(G,M)>> M is a variable and Existential by Double Variable Instantiation Rule of> UNIFY().>> - - - - - - - - - - - - - - ->INSERT  A STEP:STEP 6aG: ~DERIVE(G,  [G | M] )G is the HEAD of M by definition.  (either 1st or last element)M are the REMAINING TAIL of deductions back to the axioms.[G <- <M>][G <- N <- <O>]...[G <- N <- P <- ... <- AXIOMS ]Now M is strictly FREE as it doesn't contain G as an element in it'sdeduction list.and 6a reduces to 6 below.>> STEP 6:  M IS A FREE VARIABLE>>   G: ~DERIVE(G,M)>> is a null statement that will return>> SUBGOAL:  M?>> i.e. When parsed by a clever logic compiler, Godel's Statement will return a> Query in response>> [PROVER]- "Why is sentence G not derivable?">> Herc>> --> if( if(t(S),f(R)) , if(t(R),f(S)) ).>     if it's sunny then it's not raining> ergo>        if it's raining then it's not sunny
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